1. Kites, Trapezoids, Midsegments
Geometry
Regular Program SY
Source:
Discovering Geometry (2008) by Michael Serra

2. Definitions
Imagine 2 adjacent isosceles triangles.

3. Kite Angles Conjecture: The non-vertex angles of a kite are congruent.
Kite Properties
Kite Angles Conjecture:
The non-vertex angles of a kite are congruent.
Kite Diagonals Conjecture:
The diagonals of a kite are perpendicular. M A T H

4. Kite Angle Bisector Conjecture:
Kite Properties
Kite Angle Bisector Conjecture:
The vertex angles of a kite are bisected by a diagonal. M A T H

5. Kite Diagonal Bisector Conjecture:
Kite Properties
Kite Diagonal Bisector Conjecture:
The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal. M A T H

6. Definitions

7. Trapezoid Consecutive Angles Conjecture:
Trapezoid Properties
Trapezoid Consecutive Angles Conjecture:
In a trapezoid, the consecutive angles between the bases are supplementary.

8. Isosceles Trapezoid Conjecture:
Trapezoid Properties
Isosceles Trapezoid Conjecture:
In an isosceles trapezoid, the base angles are congruent.
*Converse of Isosceles Trapezoid Conjecture:
In a trapezoid, if the base angles are congruent, then the trapezoid is isosceles.

9. Isosceles Trapezoid Diagonals Conjecture:
Trapezoid Properties
Isosceles Trapezoid Diagonals Conjecture:
In an isosceles trapezoid, the diagonals are congruent.

10. Real Life Connection

11. Real Life Connection

12. Book Exercises

13. Book Exercises
Answer the following:
p. 271

14. Book Exercises
Answer the following:
p. 271

15. Book Exercises
Answer the following:
p. 271

16. Book Exercises
Answer the following:
p. 271

17. Book Exercises
Answer the following:
p. 271

18. Book Exercises
Answer the following:
p. 271

19. Book Exercises
Answer the following:
p. 271

20. Book Exercises
Answer the following:
p. 271

21. What is a midsegment of a triangle ?
Definitions
What is a midsegment of a triangle ?

22. EXAMPLES NON-EXAMPLES

23. “3rd side” – side not connected to midsegment
Definitions
What is a midsegment of a triangle ?
A midsegment of a triangle is…
a segment whose endpoints are the midpoints of two sides of a triangle.
“3rd side” – side not connected to midsegment

24. What is a midsegment of a triangle ?
Definitions
What is a midsegment of a triangle ?

25. What is a midsegment of a trapezoid ?
Definitions
What is a midsegment of a trapezoid ?

26. What is a midsegment of a trapezoid ?
Definitions
What is a midsegment of a trapezoid ?
A midsegment of a trapezoid is…
a segment whose endpoints are the midpoints of the non-parallel sides (legs) of a trapezoid.
Can you draw non-examples of a midsegment of a trapezoid?

27. Midsegment Properties
Triangle Midsegment Conjecture:
In a triangle, the midsegment is parallel to the third side, and measures half the length of the third side.
Trapezoid Midsegment Conjecture:
In a trapezoid, the midsegment is parallel to the bases, and measures half the sum of the lengths of the bases.

28. Book Exercises
Answer the following:
p. 277

29. Book Exercises
Answer the following:
p. 277

30. Book Exercises
Answer the following:
p. 277

31. Book Exercises
Answer the following:
p. 277

32. Book Exercises
Answer the following:
p. 277

33. Book Exercises
Answer the following:
p. 277

34. Book Exercises
Answer the following:
p. 277

35. Book Exercises
Answer the following:
p. 277

36. Book Exercises
Answer the following:
p. 277

37. MORE Exercises
Answer the following:
p. 304

38. MORE Exercises
Answer the following:
p. 304

39. MORE Exercises
Answer the following:
p. 304

40. MORE Exercises
Answer the following:
p. 304

41. MORE Exercises
Answer the following:
p. 304

42. MORE Exercises
Answer the following:
p. 304

43. MORE Exercises
Answer the following:
p. 304

44. ALWAYS. SOMETIMES. NEVER.
MORE Exercises
ALWAYS. SOMETIMES. NEVER.
The diagonals of a kite are congruent. S
Consecutive angles of a kite are supplementary. N
The diagonal connecting the vertex angles of a kite divides the kite into two congruent triangles. A
The diagonals of a trapezoid bisect each other. N
The three midsegments of a triangle divide the triangle into 4 congruent triangles. A
The midsegment of a trapezoid is perpendicular to a leg of the trapezoid. S